Which of the following cubes can be made from these nets?
Age 14 to 18 Challenge Level:
This activity involves a Rubik's
cube which has been opened out into a net. With this activity it
will help if you have already spent some time playing with an
ordinary 3-dimensional Rubik's cube. It provides excellent training
of your visualisation skills.
To play the net you simply click on the centre of each face to make
it twist anti-clockwise.
You may like to try these activities:
1. Click on the White face1, 2, 3 and 4 times. Try to understand
how it is moving squares on the other faces.
2. Repeat for the other faces to try to understand how the net is
3.Click on the 'Scramble' button for 1 move. The effect of this is
to make one randomly chosen anticlockwise twist of a face. Can you
spot which face must have been twisted? Can you work out how to
undo the effect of this twist?
3. Now try scrambling by 2 moves. Can you spot which moves were
randomly chosen? How would you undo the effects of these
4. You may like to try scrambling by 3 or 4 moves.If you make a
mistake trying to undo the scramble you can reset the last
scrambled state to try again.
Once a net is highly scrambled (by, say 15 moves) it is impossible
to see how the net became scrambled.
A much more difficult challenge is to try to solve a highly
scrambled net so that an entire face is completed.
Once the entire face is completed you can try to solve so that
the squares adjacent to the completed face are all in the correct
place, as in the following picture:
Progressing beyond this level of solution
is very difficult without a systematic approach. To explore this
idea please see the problem
Solving the Net
Other ideas for playing with the net are:
1) Experiment to find sequences of your own which have nice
properties on the net. For example, can you find the12 twists which
create this net configuration?
2) If you click on a square on the net then it will be blacked out.
Try blacking out the corners, making a few twists and then predict
the colour of the blacked out squares. Click on them to see if you
were correct. This is a great way of exercising your visual mind
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embed rich mathematical tasks into everyday classroom practice.